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My question is given a set of angles in the form of degrees minutes and seconds once finding the mean how do you find the standard deviation.

I know how to find the average or mean of a set (see below) but i'm not sure how to find the standard deviation.

For example say we have the following set of angles:

$$39^\circ 15'01''$$ $$39^\circ 14'15''$$ $$39^\circ 14'32''$$

The average is $39^\circ 14'36''$. Now, how do I find the standard deviation.

I looked at the wiki page, but can't make since of it using degrees minutes seconds instead..

Dmitri.Mendeleev
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2 Answers2

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Your first number is $39 + \dfrac{15}{60} + \dfrac{1}{60^2} = 39.250277777\ldots$. Deal similarly with the others.

And remember to do as little rounding as possible at least until the last step. Rounding should always wait until the last step except when you know how much effect it will have on the bottom line. One way to do avoid it is to work with exact fractions. (Except that the seconds are of course probably rounded . . . .

Michael Hardy
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  • I know how to convert to decimal, my calculator can do this for me if I wish. I just need to know how to find the standard deviation. I know I subtract the mean from each individual number, square them, then and add them all together, then divide them all by n, and take the square root. But how in the world would I do this if I had a huge set of data and no computer? – Dmitri.Mendeleev Feb 21 '13 at 01:39
  • Generally, finding standard deviations with large data sets and no computer is labor-intensive. I believe there are various shortcuts, but even so it can be expensive if the data set is large. – Michael Hardy Feb 21 '13 at 01:50
  • What about a not so large set, like say 15 angles? Is the method I described above my best bet? – Dmitri.Mendeleev Feb 21 '13 at 01:53
  • If I had a huge set of data and no computer, I'd go to the nearest computer store and buy a computer. What's the point of trying to do a job without the proper tools? – Robert Israel Feb 21 '13 at 01:55
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This is a link to the Standard Deviation formula of a sample, applying it to your example:

√(((15′01″ - 14′36″)^2+(14′15″ - 14′36″)^2+(14′32″ - 14′36″)^2)/3-1)

= 23.26″

Mohammed Abdellateef
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